Extreme statistics for time series: Distribution of the maximum relative to the initial value

The extreme statistics of time signals is studied when the maximum is measured from the initial value. In the case of independent, identically distributed (iid) variables, we classify the limiting distribution of the maximum according to the properties of the parent distribution from which the variables are drawn. Then we turn to correlated periodic Gaussian signals with a 1/f^alpha power spectrum and study the distribution of the maximum relative height with respect to the initial height (MRH_I). The exact MRH_I distribution is derived for alpha=0 (iid variables), alpha=2 (random walk), alpha=4 (random acceleration), and alpha=infinity (single sinusoidal mode). For other, intermediate values of alpha, the distribution is determined from simulations. We find that the MRH_I distribution is markedly different from the previously studied distribution of the maximum height relative to the average height for all alpha. The two main distinguishing features of the MRH_I distribution are the much larger weight for small relative heights and the divergence at zero height for alpha>3. We also demonstrate that the boundary conditions affect the shape of the distribution by presenting exact results for some non-periodic boundary conditions. Finally, we show that, for signals arising from time-translationally invariant distributions, the density of near extreme states is the same as the MRH_I distribution. This is used in developing a scaling theory for the threshold singularities of the two distributions.Comment: 29 pages, 4 figure

Positive definite metric spaces

Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended to infinite metric spaces in several a priori distinct ways. This paper develops the theory of a class of metric spaces, positive definite metric spaces, for which magnitude is more tractable than in general. Positive definiteness is a generalization of the classical property of negative type for a metric space, which is known to hold for many interesting classes of spaces. It is proved that all the proposed definitions of magnitude coincide for compact positive definite metric spaces and further results are proved about the behavior of magnitude as a function of such spaces. Finally, some facts about the magnitude of compact subsets of l_p^n for p \le 2 are proved, generalizing results of Leinster for p=1,2, using properties of these spaces which are somewhat stronger than positive definiteness.Comment: v5: Corrected some misstatements in the last few paragraphs. Updated reference

Knife-edge conditions in the modeling of long-run growth regularities

Balanced (exponential) growth cannot be generalized to a concept which would not require knife-edge conditions to be imposed on dynamic models. Already the assumption that a solution to a dynamical system (i.e. time path of an economy) satisfies a given functional regularity (e.g. quasi-arithmetic, logistic, etc.) imposes at least one knife-edge assumption on the considered model. Furthermore, it is always possible to find divergent and qualitative changes in dynamic behavior of the model – strong enough to invalidate its long-run predictions – if a certain parameter is infinitesimally manipulated. In this sense, dynamics of all growth models are fragile and "unstable"

The theory and method of comparative area studies

Though many now downplay the tension between area studies and disciplinary political science, there has been little substantive guidance on how to accomplish complementarity between their respective approaches. This article seeks to develop the idea of comparative area studies (CAS) as a rubric that maintains the importance of regional knowledge while contributing to general theory building using inductive intra-regional, cross-regional, inter-regional comparison. Treating regions as theoretically-grounded analytical categories, rather than inert or innate geographical entities, can help inform both quantitative and qualitative attempts to build general theory.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Fiscal Policy, Private Investment and Economic Growth: Evidence from G-7 Countries

Measuring the effects of fiscal policy on economic growth is difficult, because fiscal policy variables are influenced by changes in income. This paper uses an unbalanced panel data set for G-7 countries for the period 1965-2000 that includes annual estimates of cyclically adjusted government expenditures, capital outlays, income tax revenues, indirect tax revenues, corporate tax revenues and social security tax revenues, based on definitions developed by OECD revenue statistics. The percentage share of these estimates in GDP is used to investigate the effects of fiscal policy on economic growth, and results are compared with regression results that use 5-year averages of cyclically unadjusted variables. The empirical results from both sets of regressions suggest that only taxes on household income and government expenditures have negative effects on per capita income growth. We consolidate our findings by showing that both government expenditures and income taxes have distortionary effects on private investment

An OLG model of growth with longevity : when grandparents take care of grandchildren

By assuming that grandparents take care of grandchildren, this paper aims at studying the effects of longevity on long-term economic growth in a model with overlapping generations and endogenous fertility. We show that an increase in longevity may: (i) reduce the long-term economic growth; (ii) increase the supply of labour, and (iii) cause fertility either to increase of decrease depending on the size of time spent by grandparents to rise grandchildren. These findings also hold in an endogenous growth setting a` la Romer (J Polit Econ 94:1002–1037, 1986).info:eu-repo/semantics/publishedVersio

Is complexity leadership theory complex enough? A critical appraisal, some modifications and suggestions for further research

Scholars are increasingly seeking to develop theories that explain the underlying processes whereby leadership is enacted. This shifts attention away from the actions of ‘heroic’ individuals and towards the social contexts in which people with greater or lesser power influence each other. A number of researchers have embraced complexity theory, with its emphasis on non-linearity and unpredictability. However, some complexity scholars still depict the theory and practice of leadership in relatively non-complex terms. They continue to assume that leaders can exercise rational, extensive and purposeful influence on other actors to a greater extent than is possible. In effect, they offer a theory of complex organizations led by non-complex leaders who establish themselves by relatively non-complex means. This testifies to the enduring power of ‘heroic’ images of leader agency. Without greater care, the terminology offered by complexity leadership theory could become little more than a new mask for old theories that legitimize imbalanced power relationships in the workplace. This paper explores how these problems are evident in complexity leadership theory, suggests that communication and process perspectives help to overcome them, and outlines an agenda for further research on these issues